The deputy chief executive of France Telecom today resigned in the wake of a spate of staff suicides that unions have blamed on a bullying management style and brutal approach to restructuring.

The former state monopoly, now Europe's third-biggest phone company, has seen its brand name, Orange, suffer a public relations disaster as 24 workers have killed themselves in shocking circumstances in the last 18 months, with at least a dozen others making failed attempts to take their lives. Some staff were found dead in their workplace or left harrowing notes blaming the company for "management by terror" and bullying.

In the latest death, a 51-year-old threw himself off a bridge in the Alps after being moved from a back-office job to one in a call centre. Previously, a 32-year-old jumped from her office in front of colleagues at the end of the working day. Both left notes blaming unbearable working conditions and enforced job changes.

After weeks of public outcry and calls by the socialist opposition for the scalps of the company's leadership, France Telecom's number two, Louis-Pierre Wenes, today stepped down.

Nicknamed "cost-killer", Wenes was the mastermind behind a restructuring and modernisation drive to cut costs by €1.7bn (£1.55bn) by the end of 2011. Under government pressure, France Telecom has put in place measures to monitor and counsel staff thought to be suicidal, and temporarily frozen 500 employee transfers that were part of the restructuring plans. That freeze was today extended until the end of the year.

The company was last night in talks with unions, which have maintained calls for two days of strike action this week in protest at the working conditions and restructuring plans. Unions welcomed the departure of Wenes but said it must be followed by a change in management style. Sebastien Crozier, of the CGC-UNSA union, said: "We think that conditions have now been met for a change of strategy."

Didier Lombard, the France Telecom chairman and chief executive who has warned of a "spiral of death" at the company, has retained his post and the backing of the French state, which still owns a 27% stake.

Lombard has been criticised by unions for his poor choice of language in describing a "suicide trend" at France Telecom. The company was further embarrassed today when the website Mediapart released a video showing Lombard telling a management meeting this year that "those who think they can just stick to their routine and not worry about a thing are sorely mistaken".

He went on to suggest that staff outside Paris spent their time at the beach, fishing for mussels, adding those days were "over". France Telecom brushed off Lombard's comments as a joke between colleagues. With the company adamant that its restructuring must continue if it is to compete with European rivals, Wenes was replaced by Stéphane Richard, a former chief of staff at the French finance ministry and a close friend of President Nicolas Sarkozy.

A spokesman for Sarkozy's ruling UMP party welcomed Wenes's resignation as "a very important move".

France Telecom has 100,000 employees in France, many of whom still have protected civil servant contracts. Unions have warned some staff with secure public sector status find their working conditions are made miserable and that they are deliberately rotated or demoted to spur them to resign. The company laid off some 22,000 people between 2006 and 2008.

The company has agreed to the French labour ministry's order that an official monitor its health and safety meetings in the wake of the suicides.